JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 25 February 2021, Shift 2, Maths Q89

Question 89 of 90 in this shift, Maths question 29 of 30, Section B.

A line is a common tangent to the circle

(x-3)^2 + y^2 = 9

and the parabola

y^2 = 4x

. If the two points of contact (a, b) and (c, d) are distinct and lie in the first quadrant, then

2(a + c)

is equal to ________.

Official answer

NTA final key.

Chapter: Conic Sections
Topic: Circle Tangents
Idea tested: Common Tangent to Circle and Conic

Same idea in other shifts

Asked 9× in all

10 Apr 2023, Shift 1 · Q29Let a common tangent to the curves $y^2=4x$ and $(x-4)^2+y^2=16$ touch the curves at the points P and Q. Then $(PQ)^2$ is equal to…MediumNumerical value
10 Apr 2023, Shift 2 · Q13Let a circle of radius $4$ be concentric to the ellipse $15x^2 + 19y^2 = 285$ . Then the common tangents are inclined to the minor axis of…HardSingle correct
28 Jul 2022, Shift 2 · Q85Two tangent lines $l_1$ and $l_2$ are drawn from the point (2, 0) to the parabola $2y^2=-x$ . If the lines $l_1$ and $l_2$ are also tangent…HardNumerical value
24 Jun 2022, Shift 1 · Q5Let $x^2+y^2+Ax+By+C=0$ be a circle passing through $(0, 6)$ and touching the parabola $y=x^2$ at $(2, 4)$ . Then $A+C$ is equal to ______.HardSingle correct
25 Jun 2022, Shift 1 · Q16If $y=m_1x+c_1$ and $y=m_2x+c_2$ , $m_1\neq m_2$ are two common tangents of circle $x^2+y^2=2$ and parabola $y^2=x$ , then the value of…HardSingle correct
26 Jun 2022, Shift 1 · Q23Let the common tangents to the curves $4(x^2 + y^2) = 9$ and $y^2 = 4x$ intersect at the point Q. Let an ellipse, centered at the origin…HardNumerical value
31 Aug 2021, Shift 2 · Q89A tangent line L is drawn at the point $(2, -4)$ on the parabola $y^2 = 8x$ . If the line L is also tangent to the circle…MediumNumerical value
26 Feb 2021, Shift 2 · Q90Let L be a common tangent line to the curves $4x^2+9y^2=36$ and $(2x)^2+(2y)^2=31$ . Then the square of the slope of the line L is…HardNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.